She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) Marla! Marla! Hey, wait! Wait! I gotta talk to you! Marla! Marla! Your bald freaks hit me with a fucking broom! They almost broke my arm! They were burning their fingertips with lye. This needs a tremendous act of faith on your part, but hear me out. - Here comes an avalanche of bullshit. (..)1999 Fight Club
(..) Without pain or sacrifice, we would have nothing. I tried not to think of the word searing of flesh. Stop it! This is your pain, this is your burning hand. I'm going to my cave to find my power animal. No! Don't deal with this the way those dead people do! Come on! - I get the point! (..)1999 Fight Club